Associations between the rates of maturation and growth in the short bones of the
hand.

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Associations between the Rates of Maturation and
Growth in the Short Bones of the Hand
A. F. ROCHE AND G . H. DAVILA
The Fels Research Institute, Yellow Springs, Ohio 45387
ABSTRACT
Serial radiographs of the hand-wrist were used to analyze the associations within bones between the rates of change i n skeletal maturity, diaphyseal and
epiphyseal lengths and diaphyseal width. In previous studies of these children, it has
been shown that these rates are linear i n relation to chronological age. The associations between the rates of change i n these parameters were analyzed using the slopes
( b values) for regression lines fiitted to the data in each child. In individual bones,
most of the correlation coefficients were moderate to low; some were negative. For most
associations in each sex they were relatively high for metacarpal 11. The rates of skeletal
maturation and diaphyseal elongation were correlated more highly in the girls than
in the boys but the rates of skeletal maturation and epiphyseal elongation were correlated more highly i n the boys. When bones were considered i n groups, relatively high
correlations were noted for the metacarpals and ray 11, lower correlations were common
for the middle and distal phalanges. There was no evidence of real neighborhood effects
but marginal effects were present.
Although skeletal maturity is assessed
independently of size (Greulich and Pyle,
'59), many consider skeletal maturation
and skeletal elongation to be associated so
closely that levels of skeletal maturity allow reliable predictions of trunk elongation, diaphyseal elongation, and growth in
stature. Some predict trunk elongation to
assist the management of scoliosis or to
estimate the effects of spinal fusion using
the skeletal maturity of the hand-wrist
(Anderson et al., '65). The same measure
of skeletal maturity is used to predict diaphyseal elongation at the distal end of
the femur or the proximal end of the tibia
prior to epiphyseodeses (Anderson et al.,
'63). Commonly, predictions of mature
stature are based on the maturity of the
hand-wrist (Bayley and Pinneau, '52). The
reliability of all these predictions depends
upon high correlations between the skeletal
maturity of the hand-wrist and potentials
for elongation elsewhere in the skeleton.
If, in fact, these were highly correlated, it
would be expected that high correlations
would occur between the rates of maturation and elongation in hand bones.
There is a need for reliable predictions
of craniofacial growth (Hixon, '68). These
predictions could be based on hand-wrist
skeletal age although, apparently, the level
of skeletal maturity is associated with only
the timing and not the amount of facial
growth (Hunter, ' 6 2 ) . Much craniofacial
AM. J. PHYS.ANTHROP.,33: 349-356.
growth, like the increase in diaphyseal
width, occurs by subperiosteal apposition.
Consequently, the levels of association
within bones between the rates of maturation and the rates of increase in diaphyseal
width might indicate whether hand-wrist
skeletal maturity would be useful in craniofacial growth prediction.
There is no literature directly relevant to
correlations between the rates of maturation and growth within bones. The only
bone-specific observation concerns the
metatarsals in which the rates of diaphyseal elongation decelerate in girls but not
boys when the corresponding epiphyses
ossify (Roche, '64).
The rates of elongation of corresponding
diaphyses and epiphyses of the bones of the
hand, considered as a group, are negatively
correlated, despite positive correlations for
the metacarpals (Roche et al., '70). Almost
all the correlation coefficients are of low
order, indicating that one of these rates
could not be predicted reliably from the
other. The level of skeletal maturity of the
hand-wrist is determined largely by epiphyseal shape (Greulich and Pyle, '59).
Elongation is a major element in the transformation of the shapes of these epiphyses.
These considerations make i t important to
determine the extent and the directions of
the correlations between the rates of skeletal maturation and growth in individual
349
350
A. F. ROCHE AND G. H. DAVILA
bones; not only in the hand but throughout
the skeleton.
MATERIAL AND METHODS
cal age for each bone in each child. These
graphs followed a linear trend in almost
all instances (Roche and Hermann, ’70a,b;
Roche, ’70). Subsequently, regression lines
were fitted to these data and the b values
(slopes) of the first-degree polynomial
( Y = bx a ) were calculated. The present analysis is based on these b values.
The present data were derived from nonscreened radiographs of the left handwrists of “normal” children living in Melbourne, Australia (20 boys; 20 girls).
These radiographs had been taken in acFINDINGS
cordance with the instructions of Greulich
Pearson product moment correlation coand Pyle (’59). Each child had a complete
series of annual radiographs taken near efficients were calculated between the b
each birthday from the third to the thir- values within each sex. Most coefficients
teenth inclusive. Other radiographs were were of moderate to low order but some
taken three-monthly from three to four were close to zero and, in the girls, two of
years and six-monthly from four to six the coefficients between the b values for
years. Bone-specific assessments of skeletal the rates of skeletal maturation and epimaturity were made using the atlas of physeal elongation were negative (table 1).
Greulich and Pyle (’59) with some inter- Some coefficients were significantly differpolations between the standards to ent from zero. In the boys, significant
monthly intervals up to the skeletal age differences were more common for correlaof five years and to three-monthly intervals tions between the rates of skeletal maturaat later ages. The lengths of the diaphysis tion and either epiphyseal elongation or
and epiphysis of each bone and the mini- increase in diaphyseal width; in the girls
mum width of the diaphysis were mea- they were particularly common for correlations between the rates of skeletal masured to the nearest 0.5 mm.
The data (skeletal ages, diaphyseal turation and diaphyseal elongation. In both
lengths, epiphyseal lengths, diaphyseal the boys and the girls, the coefficients
widths) were graphed against chronologi- tended to be high for all correlations in-
+
TABLE 1
Coefficients of correlation between t h e rates ( b v a l u e s ) of maturation and the rates of ( 1 )
diaphyseal elongation, (2) epiphyseal elongation and ( 3 ) increase in diaphyseal w i d t h
in corresponding hand bones (20 boys; 20 girls)
Boys
Bone
Metacarpal I
Metacarpal I1
Metacarpal I11
Metacarpal IV
Metacarpal V
Proximal Phalanx I
Proximal Phalanx I1
Proximal Phalanx 111
Proximal Phalanx IV
Proximal Phalanx V
Middle Phalanx I1
Middle Phalanx I11
Middle Phalanx IV
Middle Phalanx V
Distal Phalanx I
Distal Phalanx I1
Distal Phalanx I11
Distal Phalanx IV
Distal Phalanx V
Mean T
1P
2
P
< .05.
< .a.
Diaphyseal
elongation
0.531
0.509
0.412
0.290
0.527
0.264
0.321
0.249
0.497
0.383
0.106
0.247
0.331
0.040
0.095
0.lM
0.258
0.377
0.351
0.320
Girls
Epiphyseal
elongation
Diaphyseal
width
Diaphyseal
elongation
0.303
0.690
0.565
0.616
0.590
0 447
0.446
0.373
0.377
0.466
0.263
0.562
0.501
0.648
0.621
0.067
0.339
0.658
0.145
0.473
0.508
0.763
0.732
0.636
0.447
0.433
0.586
0.412
0.120
0.193
0.242
0.283
0.318
0.045
0.213
0.578
0.599 2
0.293
0.374
0.432
0.568
0.731
0.665
0.646
0.534
0.596
0.753
0.768
0.771
0.590
0.660
0.579
0.651 2
0.460
0.035
0.560
0.561
0.572
0.577
0.609
Epiphyseal
elongation
0.586
0.555
0.565
0.323
0.456
0.254
0.126
0.141
- 0.279
0.326
0.274
0.314
- 0.176
0.185
0.592 2
0.594 2
0.316
0.3 74
0.427
0.329
Diaphyseal
width
0.594 a
0.627
0.262
0.355
0.323
0.373
0.537
0.515
0.404
0.309
0.481
0.378
0.358
0.146
0.431
0.313
0.222
0.343
0.363
0.392
351
MATURATION AND GROWTH IN HAND BONES
volving metacarpal I1 and for most involving metacarpals I and 111. For metacarpal
V, the coefficients between the rates of
skeletal maturation and both diaphyseal
and epiphyseal elongation were relatively
high also. Most of the coefficients relating
to middle phalanx V tended to be low in
both the boys and the girls.
Rank order correlations were calculated within each sex between the correlation coefficients of individual bones. In the
boys, the correlation coefficients relevant
to the rates of skeletal maturation and the
rates of either diaphyseal elongation, epiphyseal elongation or increase in diaphyseal width had rank order correlations that
were not statistically significant. In the
girls, there was a statistically significant
( P < 0.05) rank order correlation indicating an inverse relationship when the rvalues between the rates of skeletal maturation and diaphyseal elongation were
compared with the r-values between the
rates of skeletal maturation and epiphyseal
elongation. Another statistically significant
(P < 0.05) but positive rank order correlation was demonstrated when the r-values
between the rates of skeletal maturation
and diaphyseal elongation were compared
with those between the rates of skeletal
maturation and diaphyseal width increase.
None of the rank order correlations between corresponding sets of coefficients in
the boys or the girls was significant.
The means of the correlation coefficients
for all bones varied from
0.320 to
0.473 in the boys and from
0.329 to
+
+
+
+
0.609 in the girls. Those between the
rates of skeletal maturation and diaphyseal
elongation were much higher in the girls
than the boys ( P < 0.001) but those between the rates of skeletal maturation and
epiphyseal elongation were more highly
correlated in the boys ( P < 0.05). There
were no real sex differences in the mean
correlations between the rates of skeletal
maturation and increase in diaphyseal
width.
Mean correlation coefficients for groups
of bones were obtained from the correlation coefficients listed in table 1. This was
done by summing the z transforms of r
and converting the mean z to a mean T .
Within rows of bones, the highest coefficients of correlation between the rates of
skeletal maturation and diaphyseal elongation in the boys, and epiphyseal elongation
and increase in diaphyseal width in each
sex were in the metacarpals (table 2). The
row of proximal phalanges had the highest
coefficient of correlation between the rates
of skeletal maturation and diaphyseal elongation in the girls. There were low correlation coefficients for the proximal phalanges
of the girls between the rates of skeletal
maturation and epiphyseal elongation. The
correlation coefficients between the rates
of skeletal maturation and diaphyseal elongation in the girls and epiphyseal elongation in the boys were low for the distal
phalanges.
When the bones were grouped in rays
(metacarpal plus the corresponding phalanges), commonly the second ray had
TABLE 2
Coeficients of correlation between the rates of maturation and the rates of ( 1 ) diaphyseal
elongation, ( 2 ) epiphyseal elongation and ( 3 ) increase in diaphyseal w i d t h
f o r groups of bones
Boys
Diaphyseal Epiphyseal
elongation elongation
Girls
Diaphyseal
width
Diaphyseal Epiphyseal Diaphyseal
width
elongation elongation
Rows
Metacarpals
Proximal phalanges
Middle phalanges
Distal phalanges
Rays
I
I1
I11
IV
V
0.458
0.346
0.184
0.252
0.565
0.423
0.506
0.394
0.633
0.361
0.224
0.424
0.634
0.704
0.593
0.479
0.503
0.116
0.153
0.469
0.441
0.432
0.346
0.336
0.309
0.284
0.293
0.376
0.336
0.467
0.394
0.467
0.547
0.482
0.391
0.569
0.528
0.359
0.372
0.426
0.683
0.652
0.667
0.542
0.491
0.405
0.344
0.066
0.353
0.471
0.498
0.350
0.360
0.288
352
A. F. ROCHE AND G. H. DAVILA
either the highest or the lowest correlation
coefficient between the rates compared. In
both the boys and the girls, it had the
highest correlations between the rates of
skeletal maturation and increase in diaphyseal width; the corresponding correlations
tended to be low in the fourth and fifth
rays. The correlations between the rates of
skeletal maturation and epiphyseal elongation tended to be high in the first ray in
both the boys and the girls.
Mean correlation coefficients between
the rates of skeletal maturation, diaphyseal
elongation, epiphyseal elongation or increase in diaphyseal width were calculated
€or groups of adjacent and non-adjacent
bones (table 3 ) . Each pair of adjacent or
non-adjacent bones included a marginal
bone and provided findings relevant to
possible neighborhood effects. A neighborhood effect is present when adjacent
bones are correlated more highly than nonadjacent bones. The present findings do
not indicate that real neighborhood effects
were present. When the bones of the hand
were considered in rows, the mean correlation coefficients between adjacent bones
were larger than those for non-adjacent
bones only for the associations between the
rates of skeletal maturation and increase in
diaphyseal width in the boys and between
the rates of skeletal maturation and epiphyseal elongation in the girls. Most of
the other differences between the mean
correlations were very small. Within rays
of bones, the mean correlation coefficients
between adjacent bones were larger than
those for non-adjacent bones only for two
of the six comparisons made. Both in the
rows and in the rays, the differences between the coefficients for adjacent and
non-adjacent bones were not significant
statistically.
Possible marginal effects were analyzed
by calculating mean Correlation coefficients for pairs of adjacent bones. Some
of the pairs included one marginal bone
on the margin of a row or ray (e.g., proximal phalanx V, distal phalanx 11) but the
other pairs included two non-marginal
bones (e.g., one non-marginal pair was
metacarpals I11 and IV). Marginal effects
are demonstrated if the correlation coefficients between marginal pairs differ from
those between non-marginal pairs. In both
the rows and the rays, five of the six comparisons between the mean correlation coefficients for marginal and non-marginal
pairs indicated the presence of marginal
effects (table 4 ) . The direction of the differences showed that the rates of skeletal
maturation and skeletal growth were less
correlated between pairs of bones when
one of these bones was marginal. Combining the data from rows and rays, these
differences were significant statistically
(chi square = 5.33; P < 0.05) despite the
lack of marginal effects in any of the mean
correlations between the rates of skeletal
maturation and epiphyseal elongation.
DISCUSSION
In children with marked lateral differences in hand size, the larger hand tends
to be more advanced skeletally with positive correlations between the lateral differences in size and maturity (Gesell, '27;
Carter and Dockeray, '53; Anderson, '67).
However, in anisomelic children there are
no real correlations between the lateral differences in bone length and the maturity
of the same bones (Roche and French,
'70). During recovery from kwashiorkor,
TABLE 3
Mean correlations between the rates of skeletal maturation and the rates of change i n
other parameters relevant to possible neighborhood effects
Girls
Boys
Mean correlations
Diaphyseal Epiphyseal
elongation elongation
Diaphyseal
width
Diaphyseal Epiphyseal Diaphyseal
elongation elongation
width
Within rows
Adjacent
Non-adjacent
0.351
0.371
0.449
0.447
0.420
0.384
0.589
0.589
0.399
0.358
0.358
0.350
Within rays
Adjacent
Non-adjacent
0.215
0.257
0.346
0.384
0.385
0.501
0.565
0.428
0.423
0.288
0.306
0.313
353
MATURATION AND GROWTH IN HAND BONES
TABLE 4
Mean correlations between the rates of skeletal maturation and the rates of change in
other parameters relevant to possible marginal effects
Girls
Boys
Mean correlations
Diaphyseal Epiphyseal
elongation elongation
Diaphyseal
width
Diaphyseal Epiphyseal Diaphyseal
elongation elongation
width
Within rows
Marginal
Non-marginal
0.299
0.333
0.451
0.492
0.314
0.495
0.664
osia
0.398
0.262
0.385
0.395
Within rays
Marginal
Non-marginal
0.252
0.349
0.394
0.492
0.424
0.438
0.479
0.646
0.469
0.287
0.336
0.417
the skeletal maturation of the hand-wrist
as a whole and the elongation of some
hand bones are accelerated (Jones and
Dean, '56).
Despite such associations between skeletal maturation and skeletal elongation, the
present analysis has shown only moderate
to low order correlations between the rates
of maturation and the rates of increase
in some growth parameters of individual
bones. These low correlations may be due
to elongation occurring at sites that are
not important in the assessment of skeletal
maturity. Normally, the short bones of the
hand have epiphyses at one end although
some diaphyseal elongation occurs at each
end (Roche, '65; Lee, '68). Estimates of
the percentage of diaphyseal elongation
occurring at the non-epiphyseal end vary
from 13% to 3 0 % ; due in part to differences in technique, age range and the
bones studied.
Most correlation coefficients for metacarpal 1-111 were relatively high but even
these would not allow reliable predictions
of one rate from another, within the same
bone. Nevertheless, the general level of
skeletal maturity of the hand is useful in
predicting elongation elsewhere (Bayley
and Pinneau, '52; Anderson et al., '63,
'65; Roche and Wettenhall, '69). During
the age range of the present study, the
correlation coefficients between the levels
of skeletal maturity and stature range between 0.5 to 0.7 (Simmons and Greulich, '43; Simmons, '44; Low et al., '64).
The association between skeletal maturity
and stature is not as close as claimed by
Variot ( ' 0 8 ) , who stated that the epiphyses
of the bones of the hand ossified at statures
of 75 to 77 cm. However, the reported correlation coefficients between skeletal ma-
+
+
turity and stature are higher than most of
those between the rates of maturation and
elongation in individual hand bones but
are similar to those for the metacarpals.
The correlation coefficients between the
rates of skeletal maturation and diaphyseal
elongation in the boys and increase in
diaphyseal width in the girls were relatively high in the metacarpals (tables 1,2).
The correlation coefficients between the
rates of skeletal maturation and both diaphyseal elongation and increase in diaphyseal width in the boys were relatively high
in the proximal phalanges. When the hand
bones were considered in rays, relatively
high correlations were common in ray 11.
There was a tendency to real marginal effects in the correlations between the rates
of skeletal maturation and diaphyseal but
not epiphyseal growth parameters.
When bone-specific assessments are
made of the maturity of the hand-wrist, the
bone skeletal ages must be combined.
There is no agreement as to whether the
arithmetic mean or a weighted mean
should be used. Weighting could be based
on communality indices for ages of achieving particular maturity levels, for rates of
skeletal maturation and for rates of hand
bone growth. Combining data from several
sources, a system of weighting based on
these communality indices would lead to
heavy weighting of the metacarpals, proxi.ma1 phalanges 11-IV, middle phalanx IV
and distal phalanx I11 (Garn and Rohmann, '59; Roche and Hermann, '70a,b;
Roche, '70). The choice between an arithmetic and various weighted means could
be based on a pragmatic approach. For
example, stepwise regressions of the percentages of mature stature achieved in
relation to individual bone skeletal ages
3 54
A. F. ROCHE AND G . H. DAVILA
could be used to choose the best mean
skeletal age for determining the percentage
of mature stature achieved.
The much higher correlations between
the rates of skeletal maturation and diaphyseal elongation in the girls than in
the boys (P < 0.001; tables 1,2) leads to the
hypothesis that these rates would be more
highly correlated in bones outside the hand
in girls than in boys. If this were so, predictions of mature stature based on skeletal
maturity would be more reliable in girls
than boys. The sex differences in the reliability of these predictions support this
hypothesis at the ages of 12 years and
over, but not at 8 through 11 years even
after the data have been adjusted to compensate for the sex-associated differences
in skeletal maturity levels at the same
chronological ages ( Bayley and Pinneau,
'52; Roche, '68).
The highest correlations between the
rates of skeletal maturation and epiphyseal
elongation within rows of bones occurred
in the metacarpals of both the boys and
the girls (table 2). These bones have the
longest epiphyses in the hand. It was hypothesized that the correlations between
the rates of skeletal maturation and epiphyseal elongation might be influenced by
epiphyseal length so that the correlations
were higher for bones with comparatively
long epiphyses. The rank order correlations for all hand bones between the relevant correlation coefficients and mean
epiphyseal lengths at eight years were not
statistically significant in either sex, thus
disproving the hypothesis.
It can be hypothesized that neighboring
bones have similar genetic controls over
their growth and maturation and that
neighboring bones exert mechanical effects
on each other that influence growth and
maturation. If these hypotheses were correct, adjacent bones would be more alike
in their growth and maturation than nonadjacent bones (neighborhood effect). If
bones on the margins of rays or rows differ
more from adjacent bones than do nonmarginal bones (marginal effect) this
could be due to lesser mechanical influences because marginal bones lack adjacent bones on one side. Such a marginal
effect could be demonstrated, for example,
by comparing the correlation between
metacarpals IV and V with that between
metacarpals I11 and IV. It is likely that real
neighborhood effects indicate that the
bones of an area have similar genetic
and/or mechanical controls; real marginal
effects probably reflect mechanical influences arising in adjacent bones and soft
tissues.
The present study has not demonstrated
real neighborhood effects in the correlation coefficients between the rates of
skeletal maturation and growth of individual bones within the hand (table 3 )
but these effects have been noted when
the rates of maturation, elongation and
increase in width are considered separately
across hand bones (Roche and Hermann,
'70a,b; Roche, '70). There were, however,
real marginal effects indicating that the
level of association between the rates of
maturation and growth of individual bones
is altered by mechanical influences from
adjacent bones and their associated soft
tissues. It may be hypothesized that neighborhood effects, in relation to correlations
between the rates of maturation and
growth within bones, are absent not only
in the hand but throughout the skeleton.
If marked neighborhood effects did occur
throughout the skeleton, predictions of future growth for a bone would have to be
based on data derived from the same bone
or from a bone adjacent to it.
Variations between the bones of the hand
in the extents to which maturation and
growth are correlated indicate that similar
variations are likely throughout the skeleton. Consequently, predictions of mature
stature or of diaphyseal elongation near
the knee might be more reliable if based on
the skeletal maturity of the femur and
tibia. In individual children, the correlation coefficients between the ages at onset
of ossification in the hand and knee are
low (Garn et al., '66) and the skeletal
maturity levels of the hand and knee differ
by more than a year in some children
(Roche and French, '70). When the
skeletal maturity level of the knee is substituted for that of the hand-wrist in predicting mature stature, employing the
tables of Bayley and Pinneau ( ' 5 2 ) , there
is no improvement in reliability for a
group of children but there are real changes
in reliability for individual children (Roche
MATURATION AND GROWTH IN HAND BONES
and Wettenhall, '69). These tables were
designed for use with the skeletal maturity
of the hand-wrist; tables based on the skeletal maturity of the knee might be more
reliable but such tables are not available.
The present findings indicate that,
within bones, the levels of association between the rates of skeletal maturation and
skeletal elongation do not differ markedly
from the levels of association between the
rates of skeletal maturation and growth in
diaphyseal width (table 1). This could
lead to a hypothesis that, both within bones
and between bones, assessments of skeletal maturity would allow equally reliable
predictions of skeletal elongation and of
growth in diaphyseal width despite differences between cellular mechanisms and
hormonal controls of growth in length and
width of bones. This reflects the varied
nature of the indicators used to assign
Greulich-Pyle skeletal ages and evinces
the possibility of sorting these indicators
into groups that could be useful for predicting separately either endochondral growth
(length) or subperiosteal growth (width).
This distinction would be of particular importance in cranio-facial growth prediction.
ACKNOWLEDGMENT
This work was supported by grants
FR-05537, HD-04629, HD-04660 and FR00222 from the National Institutes of
Health, Bethesda, Maryland.
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